New constructions for local approximation of Lipschitz functions.II

Abstract

In this paper, some properties of the set-valued mapping D α f ( . ) connected with the new approximation method of a function f ( . ) defined in the first part of the article are given. Continuity and Lipschitz properties of D α f ( . ) are formulated. A continuous extension of the Clarke subdifferential of any function represented as a difference of two convex functions is given. For the convex case, the set-valued mapping D α f ( . ) is similar to the ε -subdifferential mapping.